Stop her nosepicking. The most common cause of nosebleeds, whether or not you're 3 years old, is trauma. The blood vessels along the nasal septum (the wall between the nostrils) are very sensitive. During the winter, the air is more dry. When the nose is dried out, it has more risk of bleeding. Use a saline nose spray during the winter to help and keep her hydrated. Otherwise, stop the nose picking habit!